Steady Shear Banding Research Articles

Shear-banding fluid(s) under time-dependent shear flows. Part II: A test of the Moorcroft–Fielding criteria

Complex systems often exhibit shear banding—the coexistence of two different states characterized by their internal structuring and local shear rates. For some of them, the heterogeneous flow corresponds to the final steady-state response, while for others, shear banding can only be transient, the banding structure healing back to a homogeneous flow in the ultimate steady state after long-lived periods. In order to explain the diversity of observations, Moorcroft and Fielding have established general criteria for the onset of banding in time-dependent flows of complex systems, ranging from polymeric fluids to soft glassy materials [Moorcroft et al., Phys. Rev. Lett. 110, 086001 (2013)]. The proposed criteria are based on the time evolution of the bulk rheological response function of the system to a given time-dependent flow protocol and are associated with a specific signature in the mechanical response. In this contribution, we test the validity of these criteria in the case of two common time-dependent flow protocols: a step stress and a shear startup. Two types of fluids are examined. On the one hand, a wormlike micelles system exhibiting steady shear banding is studied experimentally, using rheometry coupled with direct visualizations and particle image velocimetry. On the other hand, we analyze previous literature on yield stress fluids exhibiting transient shear banding. Under conditions of a constant imposed stress, for both types of fluids, the onset of banding arises in a time window compatible with the Moorcroft–Fielding criterion. However, the mechanical signature, i.e., the shape of the bulk mechanical signal as a function of time, is not the one expected within some of the specific models with which the general Moorcroft–Fielding criteria were tested numerically. Under shear startup, both types of fluids behave differently. The criterion holds for yield stress fluids, the onset of banding arising just after the stress overshoot, as expected. On the contrary, for wormlike micelles, the window of instability is delayed, even if the overshoot clearly plays a crucial role in the nucleation of shear-induced structures. Regardless of the flow protocol or the system, wall slip seems to go hand in hand with banding indicating that it is a key ingredient to take into account.

Microstructure and mechanical properties of a multilayered CoCrNi/Ti coating with varying crystal structure

Medium entropy alloys (MEAs), such as CoCrNi, have been demonstrated to combine high hardness and excellent ductility, thereby outperforming many high entropy alloys reported to date. In this study, a multilayered CoCrNi/Ti coating was deposited onto a M2 steel substrate using a DC magnetron sputtering system. Columnar grains can be observed in both the CoCrNi and Ti layers. A high density of periodic twin boundaries, aligned in a direction normal to the growth direction, was also observed within the columnar CoCrNi grains. Moreover, different crystal structures were identified for different CoCrNi layers. The outermost CoCrNi layer exhibited a FCC structure, whilst in contrast, both the middle and bottom CoCrNi layers exhibited a BCC structure. It was assumed that Shockley partial dislocations were responsible for the FCC to BCC transition occurring in both the bottom and middle CoCrNi layers. A high hardness of ~7.6 GPa and elastic modulus of ~233 GPa were determined for this multilayered coating by nanoindentation testing. Further, extraordinary damage tolerance was found in the multilayered CoCrNi/Ti coating under indentation loading. The steady shear banding behaviour during deformation may benefit energy dissipation and promote structural plasticity.

Elucidating the flow-microstructure coupling in entangled polymer melts. Part II: Molecular mechanism of shear banding

In this study, we have elucidated the molecular origin of shear banding in the entangled polymeric melts. Specifically, it is shown that the inflection point corresponding to the stress-overshoot indicates the possibility of inhomogeneity and this combined with slow orientation relaxation in step-strain start-up experiments will lead to formation of local inhomogeneity along the velocity gradient direction. Once the aforementioned inhomogeneities are created, a localized jump in entanglement density and a commensurate jump in normal stress and viscosity will lead to formation of the incipient shear banded flow structure. To this end, number of step-strain and start-up simulations with different deformation rate ramp times in the planar Couette flow with entanglement densities ⟨Zk⟩ ≥ 17 were performed to demonstrate the effect of deformation rate ramp time on the formation of local inhomogeneities and occurrence of shear banding. It has been demonstrated that if the time scale for the deformation rate to reach its steady value is larger or on the order of the orientation relaxation time of the chain, local inhomogeneities in the velocity gradient direction will not form and the linear velocity profile will prevail. Overall, the molecular mechanism of incipient shear banding as well as its evolution to steady shear banding or to a linear velocity profile (transient shear banding) is described for the first time. Moreover, our findings are in agreement with a host of prior step-strain and start-up experiments with synthetic and natural Deoxyribonucleic acid (DNA) entangled polymeric fluids.In this study, we have elucidated the molecular origin of shear banding in the entangled polymeric melts. Specifically, it is shown that the inflection point corresponding to the stress-overshoot indicates the possibility of inhomogeneity and this combined with slow orientation relaxation in step-strain start-up experiments will lead to formation of local inhomogeneity along the velocity gradient direction. Once the aforementioned inhomogeneities are created, a localized jump in entanglement density and a commensurate jump in normal stress and viscosity will lead to formation of the incipient shear banded flow structure. To this end, number of step-strain and start-up simulations with different deformation rate ramp times in the planar Couette flow with entanglement densities ⟨Zk⟩ ≥ 17 were performed to demonstrate the effect of deformation rate ramp time on the formation of local inhomogeneities and occurrence of shear banding. It has been demonstrated that if the time scale for the deformation rate to r...

Molecular Processes Leading to Shear Banding in Well Entangled Polymeric Melts.

We have performed hi-fidelity dissipative particle dynamics (DPD) simulations of shear flow of polymeric melts in a broad range of system sizes and two entanglement densities to determine the critical conditions for occurrence of both transient and steady shear banding. Here, we report, for the first time, simulation results that clearly demonstrate the consecutive steps leading to shear banding, that is, the stress overshoot drives locally inhomogeneous chain deformation and thus spatially inhomogeneous chain disentanglement; in turn, the localized jump in the entanglement density along the velocity gradient direction results in a considerable jump in normal stress and viscosity, which ultimately leads to shear banding. Overall, our observations are consistent with prior experimental studies, and an explanation for the stability of steady and transient shear banded flows is postulated based on the well-known interfacial stability mechanism of stratified polymeric fluids.

A study of shear banding in polymer solutions

In a recent letter [M. Cromer, M. C. Villet, G. H. Fredrickson, and L. G. Leal, “Shear banding in polymer solutions,” Phys. Fluids 25, 051703 (2013)], we showed the existence of a steady shear-banded velocity profile for a model polymer solution with an underlying monotonic constitutive curve. The driving mechanism is the coupling of the polymer stress to an inhomogeneous concentration profile. To further understand this phenomenon, in this paper we investigate the underlying linear instability as well as probe the model parameters and their effect on transient and steady state solutions. The linear stability analysis of the steady, base homogeneous model shows that, in opposition to diffusion, the polymer concentration moves up stress gradients in a shear flow creating a critical balance such that, for a range of parameters, an instability occurs that drives the system away from homogeneity. The simulation of the full nonlinear equations in planar one-dimensional shear reveals a window within which the linear instability manifests itself as a shear-banded flow. Unlike the case for a nonmonotonic constitutive curve for which two bands are predicted, there is no apparent selection process for a monotonic curve that sets the number of bands in planar shear. Thus, we find the possibility of greater than two bands, the number of which is determined by the ratio of the polymer correlation length to the channel width. In addition to steady shear banding, transient phenomena are also probed revealing a complicated band transition (i.e., number of bands changing in time) as well as elastic recoil in a Taylor-Couette cell, each of which have been observed in experiment. Finally, as we showed in our letter, a nonlinear subcritical instability exists resulting in multiple steady states depending upon the wall ramp speed. Here, we show that this phenomenon can occur for realistic parameter values, in particular those obtained for a particular polymer solution that has shown this multiple steady state behavior experimentally.

Steady shear banding in complex fluids

Shear banding (SB) is manifested by the abrupt “demixing” of the flow into regions of high and low shear rate. In this paper, we first relate analytically the rheological parameters of the fluid with the range of shear rates and stresses of SB occurrence. For this, we accept that the origin of shear banding is constitutive, and adopt a non-linear viscoelastic expression able to accommodate the double-valuedness of the stress with flow intensity, under certain conditions. We then implement the model for the case of pressure driven flow through a cylindrical pipe; we derive approximate expressions for the velocity profile in the two-banded regions (core and outer annular), the overall throughput in the presence or absence of “spurt”, and the radial location limits of the shear rate discontinuity.